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### Course: Arithmetic > Unit 13

Lesson 4: Adding and subtracting fractions with unlike denominators- Adding fractions with unlike denominators introduction
- Add fractions with unlike denominators
- Subtracting fractions with unlike denominators introduction
- Subtracting fractions with unlike denominators
- Adding and subtracting 3 fractions
- Solving for the missing fraction
- Add and subtract fractions

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# Subtracting fractions with unlike denominators introduction

Learn how to subtract fractions with unlike denominators. Watch the process of finding a common denominator, converting the fractions, and then performing the subtraction.

## Want to join the conversation?

- why math got to be so hard(89 votes)
- I know it́s super hard but super ez at times(26 votes)

- my question is how would u do it like step by step with divison or multiplication(25 votes)
- You multiply the numerator and denominator across for the fractions you want to multiply(14 votes)

- So you still find a common denominator even if you are subtracting.(13 votes)
- why in some questions i solve by writing out the problem and still get it wrong, but I did it exactly how it shows.(11 votes)
- How do i get the answer wrong?(7 votes)
- Maybe you need help with math? It's ok!(0 votes)

- who is Sal? I like him better than the girl.(5 votes)
- So isn't Sal just saying that when you subtract fractions that have different denominators ( 1/2 - 1/3) that you just multiply the other denominator to both of the numerators and denominators? Ex. 1/2 = 3/6, 1/3 = 2/6(4 votes)
- Why did you multiply by 3? Was it because it was 1/3 so we have to multiply by 3? For example if we have 1/4, we would have to multiply by 4 right?(2 votes)
- You are partially correct.

It is indeed because of 1 / 3, but not directly related to the denominator.

You might have missed a few lessons if you're raising this question. Check this out:

https://www.khanacademy.org/math/cc-fifth-grade-math/imp-fractions-3/imp-common-denominators-2/v/finding-common-denominators

When we want to find a common denominator between 2 fractions, we find the LCM of the denominators of the 2 fractions.

LCM(2, 3) = 6

Now, we find a number such that when it is multiplied by 2 = 6, which we can solve and find out it is 3.

Hence we multiply by 3.

The same goes to the fraction with 3.

Okay, now let's say we have 1 / 2 and 1 / 4.

LCM(2, 4) = 4

Now, we find a number such that when it is multiplied by 2 = 4, which we can solve and find out it is 2, and not 4!

(1 * 2) / (2 * 2)

= 2 / 4

For 4, we don't have to multiply by anything (Multiply by 1, to be precise).(3 votes)

- Why do i have to do math in summer my break time!?(3 votes)
- Is Subtracting Fractions just like Adding Fractions but subtracting instead of adding?(2 votes)
- yes try your best(1 vote)

## Video transcript

- [Instructor] Let's say
we wanted to figure out what one half minus one third is equal to. And we can visualize
each of these fractions. One half could look like
that where if I take a whole and if I divide it into
two equal sections, one of those two equal
sections would be a half and you see that shaded in green here. And then from that, we're
trying to subtract a third and we can visualize a third this way. That if this whole thing is a whole, I divide it into three equal sections and one of those three
equal sections is a third. So what we wanna do is
take away this gray box from this green box and figure out how we can mathematically
say what is left over. So pause this video and see
if you can have a go at this. And I'll give you a
hint, it will be useful to be able to represent
your halves and thirds in terms of a different denominator. All right, now let's work
through this together. So the way that we can approach this is to get a common denominator. If I can express both fractions in terms of the same denominator, it's going to be a lot easier to subtract. And the common denominator
that's most useful is to find the least common denominator. And the smallest number that is both a multiple of two and three is actually two times three, or six. So what if we were to
write each of these numbers in terms of sixths. So how can we rewrite one
half in terms of sixths? I always have trouble saying that. Well if I start with one
half and if I multiply the denominator by three, that's going to get us to sixths and so I don't change the
value of the fraction. I need to multiply the
numerator by three as well. As long as I multiply both the numerator and the denominator by the same thing. Well, then that's still
going to be equal to one half and you can visualize
what that looks like. If you take each of
these two equal sections and turn them into three equal sections, well then you're gonna have
a total of six equal sections or sixths. Two times three in the denominator and the part that was shaded in in green which was just one of those sections is now three times as many sections. So your one half is now
equal to three over six. And we can do the same thing over here. If we start with one third how do we express it in terms of sixths? Well to go from three to six
I would multiply it by two, and so I also wanna do
that in the numerator so that I don't change
the value of the fraction and we can visualize that. Notice, if you take all three sections and you turn each of
them into two sections you now have six equal sections. So you are now dealing with sixths, and that one section before is now going to become two sections. So this is now going to
be equal to two sixths. So we can actually rewrite things as this is the same thing as three sixths minus, minus two sixths. And what do you think that is going to be? Well if I have three of something and I subtract two of them away I'm going to be left with
one of that something. So I'm going to be left
with one sixth in this case. And we can visualize it just the way we visualized everything else. If you take two of these gray bars or two of these sections
from these three sections you're just going to be
left with one of them. This is one of the six equal sections.